THE INFLUENCE OF PARTICLE NUMBER ON MICROSTRUCTURE OF THE NiAl MODEL

This paper studies the influence of the number of particle on microstructure of the NiAl bulk model and the NiAl nano particle model by Molecular Dynamics (MD) method with the Sutton-Chen embedded interaction potential and appropriate boundary conditions. The bulk model was studied with periodic boundary conditions and the nano particle model was studied with aperiodic boundary conditions. Studies of NiAl models with 5,324 particles, 6,912 particles and 8,788 particles which were increased in temperature from 0 K to 2,000 K , then lowered from 2,000 K to 300 K with moving step dr = 0.01 have given consistent results with experimental results. The microstructure characteristics were analyzed through the radial distribution function (RDF), the coordination number, the energy, the size of particles and the common neighborhood analysis method (CNA). Results showed that the structure phases fcc, hcp and bcc appeared in the models with 5,324 particles; 6,912 particles and 8,788 particles at temperature of 300 K. Research results also confirmed that there was an influence of the number of particle on the microstructure of the models.


Introduction
Today, the CoAl alloy, NiAl alloy, etc. have been used intensively in science and technology [13]. NiAl materials play an important role because they are the essential parts in electronic equipment and industrial products. NiAl can increase the conductivity [7,11,17] of the electronic equipment. For industrial products, NiAl serves as a ceramic coat that reduces the temperature effects on the materials surface and increases the adhesion on materials. In addition, NiAl is also a material with a high melting temperature from 750 o C to 850 o C and high capacity of heat conduction and antioxidation. NiAl, therefore, has been applied in the aerospace industries, as in jet engines [4,5,14]. In recent years, NiAl material has also been of interest due to their compression resistance, high antioxidant resistance and small mass density [1][2][3]. Experimental studies of NiAl showed that the distance between atoms (molecules) in the NiAl model is 2,2 A o [6], and studies of NiAl using the simulation method revealed that the distance between Al-Al atoms (molecules) and Ni-Ni is 2,7 A o and 2,25 A o , respectively.
Our study has not only given a new understanding about the NiAl material but also proved that when the number of particles is increased, the atom (molecule) density will increase, and the crystallization of atoms (molecules) occurs when the temperature is decreased. In this paper, we focus on a detailed study of the influence of the number of particles on the microstructure of the NiAl bulk model and the NiAl nanoparticles model using the Molecular Dynamics method and the Sutton-Chen embedded interaction potential with appropriate boundary conditions. The data were analyzed in Part 2. The obtained results were compared with related experimental as well as simulation results which are presented in Part 3, and the conclusions are shown in Part 4.

Method of calculation
Initially, the NiAl bulk models with 5,324 particles, 6,912 particles and 8,788 particles were put randomly in a cubic box. These models were studied using the Molecular Dynamics (MD) [15] method with the Sutton-Chen embedded (2.1) [9,12,16] interaction potential and periodic boundary conditions. The NiAl nanoparticle models with 5,324 particles, 6,912 particles and 8,788 particles were put randomly in a spherical box. These models were studied using the Molecular Dynamics (MD) method with the Sutton-Chen embedded interaction potential with aperiodic boundary conditions.
where rij is the distance between two atoms i, j; a is the lattice constant; i is the atomic density i; Etot is the energy of the system; (rij) is the energy between two atoms i, j; F(  i) is the interaction force of atom i; rc is the disconnect radius, ε is the energy; C, M, n, N are parameters of the model. In which, parameters of the NiAl model were calculated as follows:

 
The main parameters of the models are shown in Table 1. Then, the temperature was increased to 2,000 K with a moving step dr = 0.01 in these models to break their initial crystalline structure and turn to the liquid state. At the liquid state with the temperature of 2,000 K, the temperature of the models was lowered to 300 K with a moving step dr = 0.01. At 300 K, we obtained the samples with the crystalline state for studying in this paper. The microstructure characteristics of these samples were studied using the radial , the coordination number, the energy, the size of particles and the common neighbourhood analysis method (CNA) [8,10] .

Results
The NiAl samples with 5,324 particles, 6,912 particles and 8,788 particles were studied in the same conditions of temperature, pressure, number of running steps, etc. We obtained their shapes as shown in Fig. 1 and Table 2.  The results in Tables 3 and Table 4 showed that the NiAl bulk sample with 5,324 particles had the cubic shape ( Fig.1a), and the NiAl nanoparticle sample with 5,324 particles had the spherical shape (Fig. 1b). The samples had a nanoscale size, and they were formed with two types of atoms: the Ni atoms which were blue and the Al atoms which were red. There appeared two distinct areas in the samples: the Al atoms density was large in the left area of the NiAl bulk sample, while the Ni atoms density was large in the right area; the Ni atoms density was large in the core area of the NiAl nanoparticle sample, while the Al atoms density was large in the surface area. This result showed that there were mainly couplings of the Al-Al and Ni-Ni atomic pairs, while there were a few couplings of the Ni-Al atomic pairs. The results also showed that when the number of particles in the NiAl samples increased, the size of the samples would be increased (Table 2).
To confirm this, we studied the radial distribution functions (RDF) of the NiAl samples. The results are shown in Fig. 2 and Table 2.  The results in Fig. 2 and Table 3 show that the first peak position of the radial distribution function prevailed in the NiAl samples with 5,324 particles at 300 K; the first peak height of the radial distribution function of the bulk sample was higher than that of the nanoparticle sample. When the number of particles in the samples increased to 6,912 particles and 8,788 particles, we saw that the first peak position of the radial distribution functions had unchanged value. This proved that there only existed the near range interaction in the NiAl samples. The height of the remaining peaks of the radial distribution functions changed insignificantly.
When the number of particles increased, the first peak height of the radial distribution functions of all samples increased; it only decreased in the bulk sample with 6,912 particles. This proved that when the number of particles of the bulk samples increased, the increase and decrease in the particle density were due to the transformation of their microstructure. In the nanoparticle sample, when the number of particles increased, the first peak height of the radial distribution functions increased, leading to the increase of the particle density.
To confirm that, we continued to study the couplings of Al-Al, Al-Ni and Ni-Ni atomic pairs. The results are shown in Fig. 3 and Table 4.  The results in Fig. 3 and Table 4 showed that the first peak position of the radial distribution functions of the couplings of Al-Al, Al-Ni and Ni-Ni atomic pairs prevailed in the NiAl samples with 5,324 particles at 300 K (Fig. 3). The length of the couplings changed insignificantly: the length of the couplings of Al-Al atomic pairs in the bulk sample was smaller than that of the nanoparticle sample; the length of the couplings of Ni-Al atomic pairs in the bulk sample was larger than that of the nanoparticle sample; the length of the couplings of Ni-Ni atomic pairs was the same in both samples. The results in Table 4 were consistent with the simulation results.
The first peak height of the radial distribution functions of the couplings of Al-Al and Ni-Ni atomic pairs prevailed, while it was small with the couplings of Ni-Al atomic pairs. This showed that the atoms (molecules) density of the couplings of Al-Al and Ni-Ni atomic pairs was very large, while it was very small with the couplings of Al-Ni atomic pairs. However, the first peak height of the radial distribution functions of the couplings of Al-Al and Ni-Ni atomic pairs in the bulk sample was higher than that of the nanoparticle sample, while the first peak height of the radial distribution functions of the couplings of Ni-Al atomic pairs in the bulk sample was lower than that of the nanoparticle sample. This result showed that the atoms (molecules) density of the couplings of Al-Al and Ni-Ni atomic pairs in the bulk sample was larger than that of the nanoparticle sample, but the atoms (molecules) density of the coupling of Ni-Al atomic pairs in the bulk sample was smaller than that of the nanoparticle sample.
When the number of particles increased to 6,912 particles and 8,788 particles, the distance between the two atoms in the couplings of Al-Al atomic pairs in bulk sample increased, but it decreased in the nanoparticle sample; the distance between the two atoms in the couplings of Al-Ni atomic pairs in the bulk sample decreased, but it increased in the nanoparticle sample; the distance between the two atoms in the couplings of Ni-Ni atomic pairs was the same in both samples. In the bulk sample, the first peak height of the radial distribution functions of the couplings of Al-Al and Al-Ni atomic pairs first increased then decreased, but it was in the reverse order in the couplings of Ni-Ni atomic pairs. In the nanoparticle sample, the first peak height of the radial distribution functions of the couplings of Al-Al and Al-Ni atomic pairs increased (Table 4). This result showed that when the number of particles increased in the model, the particle density would be increased, leading to the increase in the couplings of Al-Al, Ni-Al and Ni-Ni atomic pairs density. This confirmed that the influence of the number of particles on the microstructure was significant.
To simulate shape microstructure of crystal NiAl at 300 K, we used the methods common neighbourhood analytical (CNA). The results are shown in Fig. 4, Table 5a and Table 5b.  We can see from Fig. 4, Table 5a and Table 5b that there primarily existed two main types of structure fcc and hcp in the NiAl models at the temperature of 300 K, and particularly there appeared two types of structure bcc and ico in the NiAl nanoparticle model. When the number of particles in the bulk model increased, the number of structure states fcc and hcp first tended to increase then decrease (Table 5a). When the number of particles in the nanoparticle model increased, the number of structure states fcc, hcp and ico increased, except for the fact that the structure state bcc first decreased then increased (Table 5b). This result confirmed that there was a significant influence of the number of particles on the microstructure and the formation of the microstructure states fcc, hcp, bcc and ico. The main reason for that formation was the size effect. When the number of particles increased, the atoms (molecules) density increased, and this made the atoms (molecules) in the surface layer tend to be clotted. As the result, this led to the formation of the microstructure states fcc, hcp, bcc and ico in the surface layer and core layer of the model.

Conclusion
Studying the influence of the number of particles on the microstructure of NiAl samples with 5,324 particles, 6,912 particles and 8,788 particles at 300 K, we have drawn some conclusions on the NiAl bulk model and the NiAl nanoparticle model as follows: -The Sutton-Chen embedded interaction potential, the chosen boundary conditions (periodic or fixed) and parameters gave consistent results with experiments.
-The NiAl models have the nano-size, and the atoms (molecules) focus more in the core layer than in the surface layer. The existence of the two areas with large Ni and Al density leads to the different structures of the surface layer.
-Two types of structure hcp and fcc mainly exist in the NiAl models, and particularly the structure bcc and ico appear only in the nanoparticle model.
-The influence of the number of particles on the microstructure is due to the size effect. When the number of particles is increased, the atoms (molecules) density increases, while the energy of the model decreases. This leads to the increase in the coordination number both in the surface layer and in the core layer.